Find the limit of the function algebraically lim (x^2 -36 / x+6 ) x ->6
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Answer:
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Work Shown:
Part 1
Part 2
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Explanations:
- There are quite a bit of steps. I decided to break things into two parts.
- The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
- Afterward, I gave each fraction the LCD mn. I multiplied top and bottom of the first fraction by n/n. I did a similar operation to the second fraction, but with m instead.
- From there, we distribute and simplify. The mn terms cancel on the left side numerator (second step of part 2).
- The n≠m is there to prevent the denominator (n-m) from being zero. We cannot divide by zero.
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